Grauert-Riemenschneider Vanishing via modulus sheaves with transfers

TL;DR

This paper shows that the Grauert-Riemenschneider Vanishing Theorem can be derived from the theory of modulus sheaves with transfers, and provides a new way to characterize rational singularities in characteristic zero.

Contribution

It demonstrates that classical vanishing theorems follow from modulus sheaves with transfers and introduces a novel characterization of rational singularities.

Findings

Grauert-Riemenschneider Vanishing follows from modulus sheaves with transfers

New characterization of rational singularities in characteristic 0

Connections between classical theorems and modern sheaf theory

Abstract

We observe that the classical Grauert-Riemenschneider Vanishing Theorem is a direct consequence of basic results from the theory of modulus sheaves with transfers as developed by Kahn-Saito-Yamazaki. We also obtain a new characterization of rational singularities in characteristic 0.